Question

Решите систему x=5y+1 2x=8y+3

Answer 1

Ответ:

Пошаговое объяснение:

x=5y+1         Подставляем во 2 уравнение вместо х выражение 5y+1  

2x=8y+3      2*(5у+1)=8у+3

                    10у+2=8у+3

                    10у-8у=3-2

                      2у=1,у=1/2,у=0,5

х=5*0.5+1

х=3,5

Ответ:(3,5;0,5)

Answer 2

To solve the system of equations, we'll use the method of substitution or elimination. I'll demonstrate the substitution method here:

Step 1: Solve one of the equations for one variable in terms of the other. Step 2: Substitute the expression found in Step 1 into the other equation. Step 3: Solve for the variable. Step 4: Substitute the value found in Step 3 back into either of the original equations to find the other variable's value.

Let's start:

Step 1: From the first equation: x = 5y + 1

Step 2: Now, substitute the value of x from the first equation into the second equation:

2x = 8y + 3 2(5y + 1) = 8y + 3 10y + 2 = 8y + 3

Step 3: Now, isolate the variable y:

10y - 8y = 3 - 2 2y = 1 y = 1/2

Step 4: Now that we have the value of y, we can find the value of x using the first equation:

x = 5y + 1 x = 5 * (1/2) + 1 x = 5/2 + 1 x = 5/2 + 2/2 x = 7/2

So, the solution to the system of equations is: x = 7/2 y = 1/2